Mean Field Tools

A Python library for numerically solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) under common noise using elicitability, deep learning and Picard iterations.

It accompanies the paper Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise — see How to cite this work.

Features

  • Deep BSDE (Backward Stochastic Differential Equation) solvers
  • Forward-Backward SDE implementations with Picard iteration
  • Neural-network function approximators (including ResNet architectures)
  • Mean field flow measure approximations (with common-noise support)
  • Filtration tools for Brownian motion and stochastic state tracking

Installation

# Clone the repository
git clone https://github.com/fjpAntunes/mean-field-tools.git
cd mean-field-tools

# Install with Poetry
poetry install

Usage

See mean_field_tools/deep_bsde/README.md for a detailed overview of the components, and mean_field_tools/deep_bsde/script/experiments/ for runnable examples (systemic risk, portfolio hedging, economic growth, and more).

Testing

The project uses pytest for testing. Tests are organized into unit and integration tests within the mean_field_tools/deep_bsde/test/ directory.

# Run all tests
pytest

# Run specific test categories
pytest mean_field_tools/deep_bsde/test/unit/
pytest mean_field_tools/deep_bsde/test/integration/

# Run a specific test file
pytest mean_field_tools/deep_bsde/test/unit/test_function_approximator.py

Structure

  • mean_field_tools/deep_bsde/: Core library — the Deep BSDE solver and its components
    • filtration.py: Brownian motion generation and stochastic state tracking
    • forward_backward_sde.py: Forward/Backward SDE classes and Picard iteration
    • function_approximator.py: Neural-network approximators
    • measure_flow.py: Mean field flow measure approximations
    • artist.py: Plotting and diagnostics
    • script/experiments/: Example applications
    • test/: Unit and integration tests

How to cite this work

If you use this library in your research, please cite:

Felipe J. P. Antunes, Yuri F. Saporito, and Sebastian Jaimungal. Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise, 2026. arXiv:2512.14967.

@misc{antunes2026deeplearningelicitabilitymckeanvlasov,
      title={Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise},
      author={Felipe J. P. Antunes and Yuri F. Saporito and Sebastian Jaimungal},
      year={2026},
      eprint={2512.14967},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2512.14967},
}

License

MIT

Project links

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Credits

Author: Felipe José Pinto Antunes

GitHub Statistics

Data verified by PyPI on Sep 16, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License

MIT License (MIT)

Requires

Python <4.0, >=3.10

Tags

mean-field-games mckean-vlasov fbsde deep-bsde elicitability stochastic-control

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